Method and apparatus for automatic ranging with variable power telescopic gun sight

ABSTRACT

In a variable power telescope gun sight, provided with stadia and aim point at the rear focus between the ocular lens and zoom system, an aim point is located above the optic center and correlated with bullet trajectory. The distance of off set of the aim point is such that, at minimum power, the aim point is zeroed relative to the stadia for impact at minimum range, this usually being the point blank range of the projectile, and at some higher power relative to an increase in range the projectile is again zeroed, in that the projectile impact and the aim point coincide. The novel telescopic sight and method of its use are based on the observations that (1) between approximately 1/3 and 2/3 maximum range and maximum range the trajectory of a high velocity bullet is substantially linear, (2) that as magnification is increased the aim point will appear to move downwardly toward optic center and (3) that the low power and some higher power of the telescope, respectively, can be correlated with a zero at the minimum and maximum range, respectively, with reference to the stadia. Correlated in such manner, changes in magnification, in the optic sense automatically set the aim point for firing without any necessity of the observer knowing the actual distance to the target.

nited States Patent [191 Spence Jan. 1, 1974 METHOD AND APPARATUS FORAUTOMATIC RANGING WITH VARIABLE POWER TELESCOPIC GUN SIGHT [76]Inventor: Mack L. Spence, 716 Dawes Dr.,

Denham Springs, La. 70726 [22] Filed: Nov. 8, 1971 [21] Appl. No.:196,698

[52] US. Cl 356/21, 350/10, 33/246 [51] Int. Cl. G010 3/20 [58] Field ofSearch 356/20, 21; 350/10; 33/246 [56] References Cited UNITED STATESPATENTS 2,811,894 11/1957 Braker 33/246 X 3,684,376 8/1972 Lessard356/21 3,492,733 2/1970 Leatherwood 350/10 X 3,213,539 10/1965 Burris350/10 X 3,386,330 6/1968 Burris et al. 356/21 3,506,330 4/1970 Allen356/21 X 2,734,273 2/1956 Blindenbacher et a1 356/21 3,431,652 3/1969Leatherwood 356/21 UX Primary ExaminerDavid Schonberg AssistantExaminerPaul K. Godwin AttorneyLlewellyn A. Proctor [57] ABSTRACT In avariable power telescope gun sight, provided with stadia and aim pointat the rear focus between the ocular lens and zoom system, an aim pointis located above the optic center and correlated with bullet trajectory.The distance of off set of the aim point is such that, at minimum power,the aim point is zeroed relative to the stadia for impact at minimumrange, this usually being the point blank range of the projectile, andat some higher power relative to an increase in range the projectile isagain zeroed, in that the projectile impact and the aim point coincide.The novel telescopic sight and method of its use are based on theobservations that (1) between approximately 15 and 34; maximum range andmaximum range the trajectory of a high velocity bullet is substantiallylinear, (2) that as magnification is increased the aim point will appearto move downwardly toward optic center and (3) that the low power andsome higher power of the telescope, respectively, can be correlated witha zero at the minimum and maximum range, respectively, with reference tothe stadia. Correlated in such manner, changes in magnification, in theoptic sense automatically set the aim point for firing without anynecessity of the observer knowing the actual distance to the target.

7 Claims, 7 Drawing Figures ERECTORS 81 MAGNIFIERS FRONT OPTICAL m T kLENS ZOOM SYSTEM RETlCLE OCCULAR LENS j PATENIEBJAN 1W4 ERECTORS 8xFRONT FOCUS MAGNIFIERS RETICLE +-2| 22 2O OPTICAL m \M OBJECTIVE CENTEROCCULAR LENS ZOOM SYSTEM LENS INVENTOR. MACK L. SPENCE 1 Y E n N (k R o(w m N Q L L V x m Y B METHOD AND APPARATUS FOR AUTOMATIC RANGING WITHVARIABLE POWER TELESCOPIC GUN SIGHT Apparatus and method for automaticadjustment of the aim point of a variable power telescope with changesin magnification, with consequent changes in the bullet trajectory,without any necessity of the observer knowing the actual distance to thetarget. The aim point appears to move downwardly with increasingmagnification, this allowing power increases as range increases, as isdesirable for precision of aim.

Telescopic gun sights have been long known in the art, and it has becomecommonplace for sportsmen to mount such devices on small fire-arms,particularly rifles. In the standard telescopic gun sight there are twopoints of focus at which a reticle, or device which carries an aimpoint, e.g., cross hairs, can be located, viz., at the front focus orrear focus. In variable power telescopes it has now become mostdesirable to locate the reticle at the point of rear focus so that aspower is increased, the apparent size or thickness of the reticle is notmagnified, such as would tend to obscure the target.

Recently introduced telescopes which include a variable power or zoomelement include the above described improvement in reticle location, andalso builtin rangefinders of various types. In most telescopes now onthe market, various indicia defining an aim point, e.g., the point wherethe vertical and horizontal lines of cross hairs intersect, is locatedwithin the telescope at the exact optical center (the point which doesnot move when power is changed). In most commercial variable powertelescopes, once the range has been determined by use of the built-inrangefinder, the observer holds over the target to compensate for thedifference between the range at which the telescope and rifle are zeroedand that estimated for the range of the target, and then fires.

A telescope with a built-in rangefinder of the above type, now in widecommercial use, is described in US. Pat. No. 3,386,330. In the telescopedescribed therein, a target of known size is precisely circumscribedbetween stadia wires, and by change of power or magnification, thedistance of the target from the observer can be read from a scale.Knowing the range, the observer can then select the magnificationdesired and then hold over the target to compensate for the differencebetween the range at which the telescope and rifle are zeroed and thedistance to the target as determined by the known ballistics of the typeof cartridge used, and then fire. The aim point is the optical center ofthe telescope sight which is held over the target by an amount estimated to compensate for the trajectory of the bullet, or bullet drop.The. time required for adjustments of power, to estimate range, returnto a desired magnification and mentally compute hold-over obviously havetheir limitations.

Devices are now described, e.g., in US. Pat. Nos. 3,340,614 and3,492,733 which automatically adjust the trajectory of the bulletsimultaneously with power changes, i.e., the steps of changing the powerfor framing a target between a pair of stadia automatically adjusts thetrajectory for firing without any necessity of the observer knowing theactual distance to the target. Telescopic sights have thus beenpivotally mounted in relation to a gun barrel so that power adjustmentsmade in framing a target between a pair of stadia raises or lowers thetelescope with relationship to the barrel to align the optical center ofthe telescope upon the target after the adjustments are completed.Hold-over is unnecessary, and after the target is so framed, and themechanical adjustment for trajectory thus made, a pair of stationarycross hairs, one horizontal and one vertical, which cross at the opticalcenter of the telescope, is then sighted upon the target, and the gunfired.

US. Pat. No. 3,431,632 also described a telescopic gun sight whereinpower adjustments automatically compensate for bullet trajectory withoutthere being any necessity of the observer knowing the actual distancebetween himself and the target. In the device described, a scale ring isused to elevate and vertically space a pair of movable horizontal crosshairs to circumscribe a target of known size. The aim point defined bythe lower horizontal cross hair and a fixed vertical cross hair isautomatically set at the proper elevation to fix upon the circumscribedtarget. The above patents are technically superb, however, they requiremajor modification to current design of telescopes or mounts and thenon-stationary mounting gives rise to accidental displacement by roughservice or the introduction of foreign particles between cam andstationary mount stud.

The telescopic gun sight embodied by the present invention obviates manyof these disadvantages and provides further improvements over these andother known prior art telescopic sighting devices.

Among the objects of this invention are:

To provide a new and improved variable power telescopic gun sight whichcontains a rangefinder, or stadia, and means for changing magnificationpower while simultaneously automatically adjusting the reticle or aimpoint to compensate for the trajectory of the bullet, whether or not theactual distance to the target is known.

To provide a variable power telescope of the character described whereinthe reticle or aim point is located in a vertical plane above the opticcenter of the telescope, and an exact relationship is provided betweenthe eccentric reticle or aim point and an external ring which operatesto produce magnification or power changes such that increases inmagnification causes the reticle or aim point to move downwardly towardthe optic center of the telescope thereby optically compensating for thebullet trajectory at increased ranges, whether or not the actualdistance to the target is known.

To provide a telescopic gun sight of the character described wherein therelationship between the external ring which operates powermagnification changes and the reticle can be easily adjusted to matchthe type of ammunition used.

To provide a more durable telescopic gun sight of simple structure,particularly one wherein there are no complicated mechanical adjustmentsto be made by changing the alignment between the telescope and the gunbarrel during ranging and firing.

To provide a new and improved reticle with rangefinder of designparticularly useful for fitting to targets of various known sizes (fromsmall game to that of elk or moose size), adapted for rapid andefficient use by the observer, capable of both vertical and horizontalmeasurement.

These and other objects are achieved in accordance with the presentinvention which embodies improvements in telescopic gun sights,comprising the usual combination of a telescopic tube which containsobjective lens, ocular lens, erectors and magnifiers for effectingchange in magnification (i.e., a zoom system) and a power changemechanism or adjusting means for changing the magnification or power. Inthe improved combination, a reticle with aim point directly above theoptic center, with respect to image, is located within the rear focus ofthe lens system, with stadia as used for estimating distance. The aimpoint is correlated, empirically or by calculation, with the trajectoryof the gun on which the telescope is used, as determined by ballisticsdata, such that as magnification or power is increased relative to thestadia the aim point moves vertically downwardly to track the path ofthe bullet in flight as it falls due to the influence of gravity.

By locating the reticle within the rear focus between the ocular lensand the erectors and magnifiers of a variable power telescope, with aneccentric aim point directly above optic center, it is thus found thatthe aim point moves, in an optical sense, vertically downwardly withrespect to the field as power is increased. By correlation between thepaths defined by this optical change and bullet trajectory, which ofcourse is also downward, with the combination of stadia, or rangefinder,a target can be ranged with the desirable quality of allowing powerincreases as range is increased. The degree of displacement of the aimpoint is such that as magnification is increased on a linearrelationship with range, which can be read from the rangefinder, ifdesired, but whether or not the observer has any knowledge of the actualdistance to the target, compensation is automatically made for the rangeand the aim point is centered directly on the target.

The invention, and its principle of operation, will be more fullyunderstood by reference to the following detailed description of aspecific embodiment, and to the attached drawings to which reference ismade in the description. Subscripts are used to show a plurality ofsimilar parts or components.

In the drawings:

FIG. 1 depicts a side elevation view of a variable power telescopic gunsight in accordance with this invention mounted on a rifle;

FIG. 2 depicts schematically the optical system of a standard variablepower telescopic gun sight as embodied in this invention;

FIG. 3 depicts the essentials (the full field not being shown) of apreferred type of reticle cell or reticle disk which includes both aimpoint and stadia as embodied by the present invention;

FIGS. 4 and 5, taken together with the preceding fugure, depict a seriesof views illustrating the method of enabling the observer tocircumscribe and range a target using a preferred type of stadia whileautomatically setting the aiming indicia for firing, whether or not theobserver is aware of the actual distance to the target; and

FIG. 6 depicts another preferred type of reticle for automatic rangecompensation, this design providing a pair of horizontal cross hairswhich provide stadia, these intersecting with a vertical cross hair, onecross hair or aim point being at optic center and the other above opticcenter. The upper cross hairs provide an eccentric aim point forautomatic ranging and the other an aim point for conventional aiming.

FIG. 7 depicts a ring scale with indicia markings correlating the rangeto target as determined by stadia, which would allow the use of thereticle on arms having vastly different trajectories. In this case thering scale is marked according to decrease from maximum range.

Referring to FIG. 1 there is shown a variable power telescopic gun sightor telescope 10 mounted via clamps 8 8 on a rifle 9, the latter per seforming no part of the present invention. The telescope 10 includes theconventional barrel 11, an eyepiece 12, an objective 13 and anadjustment ring 14, provided with a handle 15 to facilitate adjustmentand operation of internal linkage (not shown) which actuates a zoomelement within the telescope so that the target image can be made tolook larger or smaller in proportion to the field.

The optical system, which is depicted schematically by reference to FIG.2, also includes the conventional objective lens, ocular lens anderectors and magnifiers which constitute a zoom system. In accordancewith this invention the reticle, with its eccentric aim point, and thestadia or rangefinder are located within the rear focus of the opticalsystem rather than within the front focus. Reticle 20 with its eccentricaim point 21 above optical center 22, with stadia or rangefinder, incombination with the conventional optic system described, constitutesthe apparatus features of the present invention. The method andprinciples of circumscribing and ranging a target using a preferred typeof stadia or rangefinder which in the optic sense automatically sets theaim point 21 for firing, whether or not the observer is actually awareof the distance to the target, is hereinafter described.

A preferred type of reticle, which can be illustrated by reference toFIG. 3, comprises a reticle cell, preferably a disk 20 constituted ofany suitable transparent material such as plastic or glass, the diskbeing generally flat or of piano form. The transparent reticle disk 20is scribed with a vertical line 25 and horizontal line 24, or indiciamarks, which intersect to provide an eecentric aim point 21, or pointwhich lies above the optic center 22 which is also generally thegeometric center of the disk. A diaganol line or indicia mark 23 joinshorizontal line 24 at a 45 angle, and the segment of horizontal line 24lying below diaganol line 23 is scribed with numerals or other indiciarepresentative of the vertical distances between lines 23, 24 at anygiven point on the horizontal scale. (Horizontal distances can also bemeasured between the point of intersection of lines 23, 24 and a pointlocated on the horizontal scale.)

The vertical distances between lines 23, 24 define stadia and, at apreselected magnification, are a measure of distances betweencorresponding points within the field of view. When a target of knownheight, at such magnification, is framed between a pair of verticalyaligned points lying on lines 23, 24 respectively, therefore, thedistance to the target is known, and it has been conventional to providemeans whereby such range could be read from a scale. In accordance withthe present invention, however, it is unnecessary to actually know thedistance to the target. Instead, the eccentric aim point isautomatically moved downwardly, in the optic sense, in response to powerincreases, or conversely upwardly in response to power decreases suchthat at the moment the target is framed the aim point is set forsighting and firing.

The technique of sighting and firing is best illustrated by reference toFIGS. 3 through 5, wherein it is assumed that both the telescope andrifle have been zeroed at maximum magnification to frame and strike atarget at 400 yards distance, and that the scribed numerals alonghorizontal line 24, lying vertically below points on line 23, are readin inches. The observer sights in on a circle or bulls eye known by himto be inches in diameter as shown in FIG. 3. The target does not fitbetween lines 23, 24 at the 15-inch scale, but is too small.Magnification is too low, e. g., 4 power. The observer knows, therefore,that the target is far away and that if a shot were fired that it wouldfall too low. The power is therefore increased, e.g., to 8 power, thefull power of the telescope, until the target fits the l5-inch scale asshown by reference to FIG. 4. The range is known or can be easilydetermined, but this is immaterial, for the aim point 21 is, in theoptic sense moved downwardly in the field, a distance shown by thedifference between the arrows, compensating for bullet trajectory sothat the muzzle of the rifle is raised when the shot is fired as shownby reference to FIG. 5.

A preferred type of reticle design is also described by reference toFIG. 6. A parallel pair of horizontal cross hairs 26,27 form stadia, thelower cross hair 27 being located at optical center. The point ofintersection of vertical cross hair 28 forms an off-set air point forautomatic range compensation, the distance between the cross hairs 26,27being used to span an object of known dimension. The compensation isgeneraliy from about 4 to 30 inches above optical center at 100 yards,and preferably from about 4 to 17 inches above optical center at 100yards. For most sporting purposes, compensation of from about 6 to 12inches above optical center at 100 yards on lowest availablemagnification is most preferred. The point of intersection of crosshairs 27,28 forms an aim point for conventional firing.

Referring to FIG. 7, there is shown a power selector ring scribed withan indicia scale representative of a range of values between a maximumcompensated range at full magnification (M and a minimum range at lowmagnification (M,). For example, in utilizing a scope where maximummagnification is three times the power at minimum magnifieation, i.e.,in a 3X-9X variable power telescope, M could be conveniently assigned avalue of I .0 and M L a value of 0.33. The power is linear within thisrange and hence the witness mark could be used to clearly indicate therange of values representative of distances in terms of fractional unitsbetween minimum and maximum range, or fractional power units between 3Xand 9X.

The present invention is based on the recognition that, in the opticsense, when the magnification of a variable power telescope with anon-magnifying reticle is changed, all points outside the optical centerof the image will appear to shift inversely with power change in aone-to-one ratio, e.g., points 6 inches apart at 4 power become 2 inchesapart at 12 power. The change in an aim point located above opticcenter, in conjunction with stadia which will also appear to movedownwardly with increases in range, although linear with respect torange, can be correlated with a given segment of a curve representativeof the trajectory of a bullet, the net change required being dependenton range, velocity, and the ballistic coefiicient of the bullet. Thus,the reticle movement is selected such that at some low power relative torange and stadia it is zeroed for tra-.

inches jectory and at some higher power relative to range increase it isalso zeroed by the downward movement of the aim point. Thus, the lowpower magnification M is zeroed at Ni /M of the maximum range and thehigher power, M is zeroed at the maximum range, and between these tworanges bullet drop is approximated very closely by the off-set reticle.The best trajectory fit by the reticle is obtained with a high power tolow power ratio of 1.5 to 3.0. The power ratio, however, is immaterialas all or only a portion of the full power can .be selected tocompensate between the two zero ranges. After a balance of maximumpossible range to allowable error has been made, the excess power ratiomay be used to extend the range finding capability and decreasehold-over normally required.

The degree of off-set may be found by trial and error or by calculation,and for most sporting purposes will be 2 to 8 minutes of angle above theoptic center at the higher magnification. This off-set is fitted to thetrajectory by the distance of off-set, or the trajectory may be fittedto the off-set by allowing the span value of the stadia and the maximumrange to become variables. The movement of the reticle from minimumzeroed range (X,) to maximum zeroed range (X is linear and continuouswith range changes. Therefore, the reti-. cle describes a straight linebetween the two points at which zero occurs, the actual trajectory is acurve and at mid-ranges lies slightly above that line described by thereticle movement between the two zero points. The error introduced isgreatest at the mid-point of minimum range and maximum range, e.g., at300 yards if the X is 200 and X is 400 yards, this error being generallyno more than I to 4 inches up to distances of 400 or more yards for highvelocity arms having muzzle velocities ranging upward of about 2,700feet per second which fire bullets having 0.30 or greater ballisticcoefficient (Ingalls). The error is generally less than the precision ofthe rifle.

The following parameters are typical for a 0.30-06 caliber rifle whenzeroed at 200 yards:

Range, in

Yards 200 250 300 350 400 Actual Bullet Path, inches +1.8 0 3.3 7.8-13.4 22.4 Reticle Movement, inches 0 0 5.5 l1.1 l6.6 22.4- Error inAim.

In the above case the M IM 2.0, the minimum range 200 yards, maximumrange 400 yards. If the variable powers M and M were 4 and 8, then at200 yards the shot would have been made at 4 power, at 400 yards on 8power, at 300 yards at 300/400 times the M (or times 8X) on 6 power,etc.

It is apparent that various modifications and changes can be madewithout departing the spirit of the present invention. The exact amountof off-set of the aim point above optic center can thus be determinedempirically or by actual calculation.

Thus, an approximate calculation of these parameters is had by thefollowing formulas:

l. The desired distance to off-set the reticle, (Q), at highest desiredmagnification, in inches at 100 yards, is defined by the formula:

Q L/ H 4 M 3) 2] 11 D/ wherein: A 1.049 where M IM 2 and 0.960 where MH/ M L 3 V muzzle velocity in thousands of feet per second B 0.50 K (I0.6/V)B B =0.l8l5 K (1 l.2/V)B K l/CV M highest magnification M lowestmagnification C ballistic coefficient (lngalls) Q off-set required athighest magnification, inches at one hundred yards X M maximum desiredrange for automatic compensation in hundreds of yards 2. The point blandrange, (X the minimum range of automatic compensation and also the rangeat which the rangefinder span is calibrated at minimum magnification, inhundreds of yards, is given by the formula:

XL (ML/MM) X XM 3. Reticle movement, (T), in inches, from one rangesetting to another is described by the following equation, the limits ofthe range being defined as X to X wherein:

X, base or zero range in hundreds of yards X range in hundreds of yardsfor which movement is desired from the base range The reticle used tocircumscribe the full field of view is preferably of circular design,though the horizontal length can also be greater than its verticallength (height). The reticle is preferably constructed as a unitarymember, and includes both the aim point and the stadia, or rangefinder.The aim point can comprise essentially any kind of indicia, cross hairs,a dot, an open juncture between converging lines, and the like. Therangefinder can be any type of device normally used for measuringdistance, but preferably the rangefinder is as described, though it canbe located virtually anywhere within the field away from the opticcenter.

It is also feasible to grind ocular lens such that the optic center doesnot correspond with the geometric center, and thus the off-set oreccentric aim point may appear centered.

[t is apparent that these and other various changes, such as in theabsolute or relative dimension of the parts, materials used, use ofconstant off-set for manufacturing purposes with allowance of maximumrange variance to fit ballistics data, and the like, can be made withoutdeparting the spirit and scope of the invention, as will be apparent tothose skilled in the art.

Having described the invention, what is claimed is:

1. In a variable power telescopic gun sight for mounting on a gunwherein is included the combination of a barrel with enclosed objectivelens, ocular lens, zoom system comprised of erectors and magnifiers,which provide a front focus and rear focus, and means mounted on thebarrel for changing the magnifying power of the telescope, theimprovement comprising locating a reticle, with stadia and a fixed aimpoint physically located above the optic center of the telescope, at therear focus between the ocular lens and the zoom system whereby powerincreases will cause the aim point to appear to move downwardly towardthe optic center of the telescope and thereby automatically compensatefor the trajectory of a bullet fired from the gun.

2. The apparatus of claim 1 wherein the aim point of the reticle isoff-set above the optic center of the telescope by a distance sufficientto correlate a linear bullet trajectory, at high magnifying power, wherethe gun is zeroed, at maximum compensated range for the gun and, atlower magnifying power, where the gun is also zeroed, with a rangedefined by the formula M /M of maximum; wherein M equals the power ofthe telescope at low power and M equals the power of the telescope athigh power magnification.

3. The apparatus of claim 2 wherein the telescope contains a reticlecell having a vertical cross hair and a pair of parallel horizontalcross hairs, one located above optic center and the other at opticcenter, the pair of horizontal cross hairs also defining stadia as wellas an off-set aim point and a conventional aim point, respectively.

4. The apparatus of claim 1 wherein the stadia are comprised of a pairof lines which adjoin one to the other at an angle of 45.

5. The apparatus of claim 4 wherein one of the lines is horizontal, andprovided with indicia indicative of the height of a target within thefield of the telescope.

6. In a variable power telescopic gun sight for mounting on a gunwherein is included the combination of a barrel with objective lens,ocular lens, zoom system comprised of erectors and magnifiers, whichprovide a front focus and rear focus, a reticle located at the rearfocus between the ocular lens and the zoom system, stadia, and means forchanging the power of the telescope, a method for correlating thetrajectory of a bullet fired from the gun comprising physically locatinga fixed aim point within the rear focus above the optic center at adistance such that, at high power, the aim point will be zeroed at themaximum range of impact of the bullet and at low power the aim pointwill be zeroed at a range defined by the formula M /M of maximum range;wherein M equals the power of the telescope at low power and M equalsthe power of the scope at high power magnification.

7. The method of claim 6 wherein at minimum power the telescope rangesfrom about one-fourth to about one-half of its maximum power.

1. In a variable power telescopic gun sight for mounting on a gunwherein is included the combination of a barrel with enclosed objectivelens, ocular lens, zoom system comprised of erectors and magnifiers,which provide a front focus and rear focus, and means mounted on thebarrel for changing the magnifying power of the telescope, theimprovement comprising locating a reticle, with stadia and a fixed aimpoint physically located above the optic center of the telescope, at therear focus between the ocular lens and the zoom system whereby powerincreases will cause the aim point to appear to move downwardly towardthe optic center of the telescope and thereby automatically compensatefor the trajectory of a bullet fired from the gun.
 2. The apparatus ofclaim 1 wherein the aim point of the reticle is off-set above the opticcenter of the telescope by a distance sufficient to correlate a linearbullet trajectory, at high magnifying power, where the gun is zeroed, atmaximum compensated range for the gun and, at lower magnifying power,where the gun is also zeroed, with a range defined by the formula ML/MHof maximum; wherein ML equals the power of the telescope at low powerand MH equals the power of the telescope at high power magnification. 3.The apparatus of claim 2 wherein the telescope contains a reticle cellhaving a vertical cross hair and a pair of parallel horizontal crosshairs, one located above optic center and the other at optic center, thepair of horizontal cross hairs also defining stadia as well as anoff-set aim point and a conventional aim point, respectively.
 4. Theapparatus of claim 1 wherein the stadia are comprised of a pair of lineswhich adjoin one to the other at an angle of 45*.
 5. The apparatus ofclaim 4 wherein one of the lines is horizontal, and provided withindicia indicative of the height of a target within the field of thetelescope.
 6. In a variable power telescopic gun sight for mounting on agun wherein is included the combination of a barrel with objective lens,ocular lens, zoom system comprised of erectors and magnifiers, whichprovide a front focus and rear focus, a reticle located at the rearfocus between the ocular lens and the zoom system, stadia, and means forchanging the power of the telescope, a method for correlating thetrajectory of a bullet fired from the gun comprising physically locatinga fixed aim point within the rear focus above the optic center at adistance such that, at high power, the aim point will be zeroed at themaximum range of impact of the bullet and at low power the aim pointwill be zeroed at a range defined by the formula ML/MH of maximum range;wherein ML equals the power of the telescope at low power and MH equalsthe power of the scope at high power magnification.
 7. The method ofclaim 6 wherein at minimum power the telescope ranges from aboutone-fourth to about one-half of its maximum power.